This document discusses rational and irrational numbers. Rational numbers can be written as fractions with whole number numerators and denominators, and include terminating and repeating decimals. Irrational numbers cannot be written as fractions and are represented by non-terminating, non-repeating decimals like the square root of 2 or pi. Both rational and irrational numbers exist on the real number line, making up the set of real numbers.
A numeral is a sign, or figure that represents a number. It is a mathematical numbering system. In other words, A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
Purpose:
This webinar by ASK aims to spread awareness about the practical use of the decimal number system in daily life to minimize errors and make calculations easier.
A numeral is a sign, or figure that represents a number. It is a mathematical numbering system. In other words, A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
Purpose:
This webinar by ASK aims to spread awareness about the practical use of the decimal number system in daily life to minimize errors and make calculations easier.
Number System.
"To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship."
- Srinivasa Ramanujan (Indian Mathematician)
A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction and division.
The real numbers are the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are “all the numbers” on the number line. There are infinitely many real numbers just as there are infinitely many in the other sets of numbers.
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4. Rational Numbers
A rational number is a number that can be written as a ratio.
That means it can be written as a fraction, in which both the
numerator (the number on top) and the denominator (the
number on the bottom) are whole numbers.
All rational numbers can
be written as a fraction.
6. Irrational Numbers
All numbers that are not rational are considered irrational.
An irrational number can be written as a decimal, but not as
a fraction.
Irrational numbers can NOT
be written as a fraction!!
7. Examples of Irrational Numbers
Non-terminating and Non-repeating decimals
(go on and on and on but don’t repeat)
SURDS (Non- Perfect Squares)
65.65971059893… 0.363765489965…
73 ≈ 8.54400374531753116…
2 ≈ 1.414213562373095048…
𝜋 = 3.141592653589…
5 ≈ 2.236067977499789696…
𝜋 = 3.141592653589…
8. Pi is a famous irrational number. People have
calculated Pi to over a quadrillion decimal places
and still there is no pattern. The first few digits look
like this:
3.1415926535897932384626433832795…
9. Both rational and irrational numbers show up on
the number line. This is why all “REAL” numbers
include rational and irrational numbers.
